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受欢迎的函数 >

extreme f(x)=x^3+2x^2-x-10

解答

极值点

f (x) = x^{3} + 2 x^{2} - x - 10

解答

极大值 (- \frac{2 + 7}{3}, \frac{34 + 14 7}{27} - 10), 极小值 (\frac{- 2 + 7}{3}, \frac{34 - 14 7}{27} - 10)

求解步骤

f^{'} (x) = 3 x^{2} + 4 x - 1

Find intervals:

递增

: - \infty < x < \frac{- 7 - 2}{3},

递减

: \frac{- 7 - 2}{3} < x < \frac{7 - 2}{3},

递增

: \frac{7 - 2}{3} < x < \infty

将

x = - \frac{2 + 7}{3}

代入

x^{3} + 2 x^{2} - x - 10 : \frac{34 + 14 7}{27} - 10

极大值 (- \frac{2 + 7}{3}, \frac{34 + 14 7}{27} - 10)

将

x = \frac{- 2 + 7}{3}

代入

x^{3} + 2 x^{2} - x - 10 : \frac{34 - 14 7}{27} - 10

极小值 (\frac{- 2 + 7}{3}, \frac{34 - 14 7}{27} - 10)

极大值 (- \frac{2 + 7}{3}, \frac{34 + 14 7}{27} - 10), 极小值 (\frac{- 2 + 7}{3}, \frac{34 - 14 7}{27} - 10)

作图

流行的例子

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